Reports suggesting the Reds have agreed a £6million deal with Chelsea are premature but the Merseysiders are resigned to the fact the 30-year-old will leave and accept it is only a matter of time before an offer comes in.
Benayoun signed an improved contract only last year but even before the departure of manager Rafael Benitez earlier this month he had already dropped several hints he wanted to leave.
Back on May 2, after the 2-0 defeat by Chelsea at Anfield, the Israeli said "he couldn't say for sure" whether he would be at Anfield on the opening day of the new campaign.
Chelsea are believed to see the former West Ham star as a direct replacement for Joe Cole, whose departure from Stamford Bridge was confirmed when the two parties failed to agree terms on a new contract after his current deal expired.
Reports claim Benayoun has already agreed in principle a four-year deal with Chelsea.
Liverpool are still continuing their search for a new manager but do not feel there is any rush to appoint Benitez's successor and have given themselves a loose timeframe until the end of the month to finalise matters.